On the Tor functor and some classes of Abelian groups (Q1821874)

The functor Tor is related to some classes of \(C_{\lambda}\)-groups, notably the IT groups, and when \(\lambda =\Omega\) the \(C_{\Omega}\) groups of balanced dimensions 1. Separate necessary and sufficient conditions are given for Tor(G,H) to be a d.s.c. group when G and H are \(C_{\lambda}\) groups. Some generalizations of the fact that balanced subgroups of G and H determine balanced subgroups of Tor(G,H) are presented.